Relatives of 43 missing Mexican students, who the authorities say were murdered by a drugs gang, have led mass protests in the capital.
The marches were largely peaceful but some protesters clashed with police near the presidential palace.
Convoys carrying the families arrived in Mexico City on Thursday after touring the country to rally support.
Many remain unconvinced by the official explanation for the students' disappearance and hope they are alive.
Masked protesters clashed with police near the airport hours before the three marches started.
Francisco Lagro, father of 19-year-old Magdaleno, one of those missing, was travelling on one of the caravans towards the capital on Thursday.
"It's been almost two months without knowing where they are. We don't know anything and we're desperate," he said.
"What are they doing? In what conditions? Do they get any water or food? Are they tied up? We have so many questions." Corruption and political violence are endemic in Mexico. In the last decade, 100,000 people have died and 27,000 people have gone missing.
Yet this single incident, the disappearance of 43 students in the southern state of Guerrero, has galvanised all of this opposition here in the centre of Mexico city.
Everyone at this march is indignant. They're angry that the government of Enrique Pena Nieto has failed to get on top of this crisis.
We don't know what happened to the 43 students. We don't even know if they're still alive.
What we do know is that they were abducted almost certainly on the orders of a local politician allied to local gangs in the state of Guerrero.
Many Mexicans have simply had enough, and they want their government to find out what happened. Thousands of people took part in three protest marches in the capital, which started at 17:00 local time (23:00 GMT).
Many thousands converged on Mexico City's main square, or Zocalo.
Several hundred protesters gathered near the presidential palace, where police tried to push them back using water cannon. There are no reports of any injuries.
In the violence near Mexico City's international airport earlier on Thursday, some 200 hooded protesters threw rocks and Molotov cocktails at police officers who had been trying to disperse them.
Many shops and businesses were reportedly closed because of the marches. Demonstrators have also called for a nationwide strike. Protests also took place in other parts of Mexico and abroad.
The abduction has galvanised opposition to rampant political corruption and violence, says the BBC's Wyre Davies in Mexico City.
Mexican President Enrique Pena Nieto has accused some of the protesters of trying to "destabilise" the state. Analysts say the issue is the biggest challenge he has faced in his two years of office.
The students, all trainee teachers, went missing after attending a protest in Iguala, Guerrero State.
Forensic tests are being carried out on bodies found in mass graves in the state.
More than 100,000 people have been killed and 27,000 have disappeared in Mexico in the last decade.
The marches were largely peaceful but some protesters clashed with police near the presidential palace.
Convoys carrying the families arrived in Mexico City on Thursday after touring the country to rally support.
Many remain unconvinced by the official explanation for the students' disappearance and hope they are alive.
Masked protesters clashed with police near the airport hours before the three marches started.
Francisco Lagro, father of 19-year-old Magdaleno, one of those missing, was travelling on one of the caravans towards the capital on Thursday.
"It's been almost two months without knowing where they are. We don't know anything and we're desperate," he said.
"What are they doing? In what conditions? Do they get any water or food? Are they tied up? We have so many questions." Corruption and political violence are endemic in Mexico. In the last decade, 100,000 people have died and 27,000 people have gone missing.
Yet this single incident, the disappearance of 43 students in the southern state of Guerrero, has galvanised all of this opposition here in the centre of Mexico city.
Everyone at this march is indignant. They're angry that the government of Enrique Pena Nieto has failed to get on top of this crisis.
We don't know what happened to the 43 students. We don't even know if they're still alive.
What we do know is that they were abducted almost certainly on the orders of a local politician allied to local gangs in the state of Guerrero.
Many Mexicans have simply had enough, and they want their government to find out what happened. Thousands of people took part in three protest marches in the capital, which started at 17:00 local time (23:00 GMT).
Many thousands converged on Mexico City's main square, or Zocalo.
Several hundred protesters gathered near the presidential palace, where police tried to push them back using water cannon. There are no reports of any injuries.
In the violence near Mexico City's international airport earlier on Thursday, some 200 hooded protesters threw rocks and Molotov cocktails at police officers who had been trying to disperse them.
Many shops and businesses were reportedly closed because of the marches. Demonstrators have also called for a nationwide strike. Protests also took place in other parts of Mexico and abroad.
The abduction has galvanised opposition to rampant political corruption and violence, says the BBC's Wyre Davies in Mexico City.
Mexican President Enrique Pena Nieto has accused some of the protesters of trying to "destabilise" the state. Analysts say the issue is the biggest challenge he has faced in his two years of office.
The students, all trainee teachers, went missing after attending a protest in Iguala, Guerrero State.
Forensic tests are being carried out on bodies found in mass graves in the state.
More than 100,000 people have been killed and 27,000 have disappeared in Mexico in the last decade.